The neutral theory of biodiversity has been criticized for its neglect of species differences. Yet it is much less heeded that S. P. Hubbell's definition of neutrality allows species to differ in their birth and death rates as long as they have an equal per capita fitness. Using the lottery model of competition we find that fitness equalization through birth-death trade-offs can make species coexist longer than expected for demographically identical species, whereas the probability of monodominance for a species under zero-sum neutral dynamics is equal to its initial relative abundance. Furthermore, if newly arising species in a community survive preferentially they are more likely to slip through the quagmire of rareness, thus creating a strong selective bias favoring their community membership. On the other hand, high-mortality species, once having gained a footing in the community, are more likely to become abundant due to their compensatory high birth rates. This unexpected result explains why a positive association between species abundance and per capita death rate can be seen in tropical-forest communities. An explicit incorporation of interspecific trade-offs between birth and death into the neutral theory increases the theory's realism as well as its predictive power.